A complete probability guide of Hold'em Poker, this guide covers all possible gaming situations. The author focuses on the practical side of the presentation and use of the probabilities involved in Hold'em, while taking into account the subjective side of the probability-based criteria of each player's strategy.

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Remember that childhood game “Odds or Evens” you used to play in order to settle important disputes such as who gets the last slice of pizza? There was only one element of skill to that game: trying to figure out what the other person would throw. But that wasn’t easy. If your opponent was savvy, that meant trying to figure out what he thought you were going to throw. And that sometimes meant figuring out what he thought you thought he (...) was going to throw. -/- Philosophers call this “thought attribution,” and top poker players are remarkably good at it. The ability to attribute thoughts to other people is especially important in the No-Limit Texas Hold’em tournaments that have, through television and the Internet, swept the globe in recent years. What is required to succeed in this game is not merely attributing “first-order” thoughts to other players, but attributing to them thoughts about your thoughts about their thoughts. In fact, that’s the minimum. The kind of thinking done by the very best players (T. J. Cloutier, Howard Lederer, and Daniel Negreanu are especially good at it) is much more complex than that. -/- In this paper, I explore the light that recent philosophical work on thought attribution sheds on the kind of thinking that goes on at the expert poker table. The paper should be revealing to poker experts and novices alike. And it should be of interest to philosophers interested in poker or thought attribution. -/- The essay is published in Poker and Philosophy, a volume of Open Court's Popular Culture and Philosophy Series. The goal of the series is to introduce philosophical themes to non-philosophers by way of particular topics of interest (in this case poker). (shrink)

This essay investigates, via the concepts of the philosophy of orientation, Annie Duke’s decision-making theory in "Thinking in Bets" and scrutinizes as to what extent one can universalize the 'orientation skill' of decision-making with regard to our everyday and professional life.

A review of a book on Popper's encounter with Wittgenstein.

This is a chapter written for a popular audience, in which I use poker as a convenient illustration of probability, determinism and counterfactuals. More originally, I also discuss the roles of rationality versus psychological hunches, and explain why even in principle game theory cannot provide us the panacea of a perfect winning srategy. (N.B. The document I have uploaded here is slightly longer than the abbreviated version that appears in the book, and also differs in a few other minor (...) details.) . (shrink)

Spoofing is the act of placing orders to buy or sell a financial contract without the intention to have those orders fulfilled in order to create the impression that there is a large demand for that contract at that price. In this article, I deny the view that spoofing in financial markets should be viewed as morally permissible analogously to the way bluffing is permissible in poker. I argue for the pro tanto moral impermissibility of spoofing and make the (...) case that spoofing is disanalogous from bluffing in at least one important regard—speculative trading serves an important economic role, whereas poker does not. (shrink)

The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book (Hutter, 2005), an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most AI researchers avoid discussing intelligence, the award-winning PhD thesis (Legg, 2008) (...) provided the philosophical embedding and investigated the UAI-based universal measure of rational intelligence, which is formal, objective and non-anthropocentric. Recently, effective approximations of AIXI have been derived and experimentally investigated in JAIR paper (Veness et al. 2011). This practical breakthrough has resulted in some impressive applications, finally muting earlier critique that UAI is only a theory. For the first time, without providing any domain knowledge, the same agent is able to self-adapt to a diverse range of interactive environments. For instance, AIXI is able to learn from scratch to play TicTacToe, Pacman, Kuhn Poker, and other games by trial and error, without even providing the rules of the games. These achievements give new hope that the grand goal of Artificial General Intelligence is not elusive. This article provides an informal overview of UAI in context. It attempts to gently introduce a very theoretical, formal, and mathematical subject, and discusses philosophical and technical ingredients, traits of intelligence, some social questions, and the past and future of UAI. (shrink)

According to a common assumption, truthfulness cannot have an intrinsic value in business. Instead, it is considered only instrumentally valuable for business, because it contributes to successful trust-building. Some authors deny truthfulness even this limited role by claiming that truth-telling is not an essential part of business, which is a sui generis practice like poker. In this article, I argue that truthfulness has indeed an intrinsic value in business and identify the conceptual confusions underlying the opposite view. My account (...) of truthfulness as a virtue shows that truthfulness is both valuable for its own sake and instrumental to further valuable goals. It helps pinpoint the implicit contradiction in claiming that truthfulness has an instrumental value only. I then challenge the reasons for considering business exempt from the constraints of truthfulness and elaborate on the analogy between game and business, which in fact supports instead of undermining my claim that business is a truthful practice. Finally, I illustrate my argument with a case study of the current crisis of trust faced by the pharmaceutical industry. (shrink)